This chapter has many phrases and ideas that are very similar to Jacob's and Nephi's writings in the Book of Mormon.
The Free Gospel Feast
Isaiah admonishes everyone to partake of the Gospel. It is free and costs us no money, yet it satisfies more than any work we can do on the earth.
I love the words, "hearken diligently unto me, and eat ye that which is good, and let your soul delight itself in fatness." (Isaiah 55:2). That passage sounds so much like Nephi when he commanded us to, "[feast] upon the word of Christ" (2 Nephi 31:20). There are also other passages in the Book of Mormon that command us to "feast" (see 2 Nephi 9:51, 2 Nephi 32:3, Jacob 2:9 and Alma 32:42).
When we ate our Thanksgiving and Christmas dinner, I could hardly stand up I was so full of food. Despite feeling so full, I could hardly wait until I was hungry again so I can eat more! How often do we spiritually eat until we are so full? I suppose if we were stuffing ourselves with spiritual ham all the time, the Lord would not have told us so often to "feast" on his words.
Sure Mercies of David
As the footnote indicates for Isaiah 55:3d, the "sure mercies of David" means the resurrection. The footnote references Acts 13:34 which refers to the resurrection. Psalms 89:2-4, 27-29 also refers to Jesus being the "mercy of David" which infers the resurrection as well.
Seek the Lord
Isaiah 55:6 says, "Seek ye the Lord while he may be found, call ye upon him while he is near." I remember my mom pointing out a scripture to me while I was in high school. It was D&C 88:83 which says, "He that seeketh me early shall find me, and shall not be forsaken."
To me, these two passages mean that we should learn the teachings of Christ and we should not put off that task for some other day. They hint at an urgency of repenting and learning the Gospel. As a teenager, I took D&C 88:83 to mean that because I had taken the time to study the scriptures and to "be a good kid" that the Lord would hold a special place in his heart for me. Maybe that was just one teenager's view of feeling like the center of the universe. But today those scriptures mean we should be more diligent in our personal repentance and scripture study and prayer and that we should feel an urgency to "seek the Lord."
Isaiah 55:7 goes along with verse 6 in that we are called to repent.
Isaiah 55:10-11 talks about precipitation from the heavens and how water does not return back up in the form of water, but in the form of fruit and bread. The water helps seeds grow which in turn grows into food for man to eat. So shall the word of the Lord go out of his mouth. It will "not return unto me void" but will come back as sanctified children of God. Alma 41:14 talks about this "boomerang effect" in that the thing you send out will come back. But the form in which it comes back depends on the person who sent it. The Lord, being perfect, sends out his word and in return, he will yield great and good fruit.